Is “King Mu obtained eight fine horses, toured the west, met the Queen Mother of the West, and composed poetry at the Jasper Lake.” true?

The third volume of the "Mu Tianzi Zhuan" records the mythical story of King Mu of the Western Zhou Dynasty driving eight fine horses on a western expedition, meeting the Queen Mother of the West at the Jasper Pool, where both composed poems in response. However, in the official history "Records of the Grand Historian: Annals of the Zhou Dynasty," there are only a few words about King Mu obtaining the horses Ji, Wen, Li, and Lu, and his western tour of inspection, without mentioning the Queen Mother of the West or the Jasper Pool meeting and other related mythical elements. The image of the Queen Mother of the West originally belongs to ancient mythology and legends, which were gradually integrated with the historical deeds of King Mu's western tour in later generations. Therefore, the plot of the Jasper Pool meeting is not historical fact of the Shang and Zhou dynasties, but rather a literary embellishment based on historical facts by later novels and records of anomalies. The original text of "Mu Tianzi Zhuan, Volume 3" reads: "天子觞西王母于瑶池之上。"